Given that dy/dx = 9y² - 4 and that y = 1 when x = 2. Find an equation expressing x in term of y.

Answer 1

WE separate variables: ∫dy/(9y² - 4) = ∫dx; 1/12lnI(3y-2)/(3y+ 2)I + C = x; 1/12 ln(1/5) + C = 2;

C = 2 + ln5/12; x = 1/12lnI(3y - 2)/(3y + 2)I + 2 + ln5/12